Einstein (157 page)

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A person “at rest” on the equator is actually spinning with the earth’s rotation at 1,040 miles per hour and orbiting with the earth around the sun at 67,000 miles per hour. When I refer to these observers being at a constant velocity, I am ignoring the change in velocity that arises from being on a rotating and orbiting planet, which would not affect most common experiments. (See Miller 1999, 25.)

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More precisely, 186,282.4 miles per second or 299,792,458 meters per second, in a vacuum. Unless otherwise specified, the “speed of light” is for light in a vacuum and refers to all electromagnetic waves, visible or not. This is also, as Maxwell discovered, the speed of electricity through a wire.

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If the source of sound is rushing toward you, the waves will not get to you any faster. However, in what is known as the Doppler effect, the waves will be compressed and the interval between them will be smaller. The decreased wavelength means a higher frequency, which results in a higher-pitched sound (or a lower one, when the siren passes by and starts moving away). A similar effect happens with light. If the source is moving toward you, the wavelength decreases (and frequency increases) so it is shifted to the blue end of the spectrum. Light from a source moving away will be red-shifted.

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Later, upon his father’s death, he became Max von Laue.

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The German phrase he used was “der glücklichste Gedanke,” which has usually been translated as “happiest” thought, but perhaps in this context is more properly translated as “luckiest” or “most fortunate.”

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Added to her 1903 physics prize, she thus became the first person to win Nobels in two different fields. The only other person to do so was Linus Pauling, who won for chemistry in 1954, and then won the 1962 Nobel Peace Prize for his fight against nuclear weapons testing.

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She was born Elsa Einstein, became Elsa Löwenthal during her brief marriage to a Berlin merchant, and was referred to as Elsa Einstein by Albert Einstein even before they married. For clarity, I refer to her as Elsa throughout.

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Although the school had been renamed, Einstein continued to call it the Polytechnic (“Polytechnikum”) and, for clarity, I will continue to use this name.

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See chapter 7. For purposes of this discussion, we are referring to a uniformly and rectilinearly accelerated reference frame and a static and homogeneous gravitational field.

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I am using the numbers in Einstein’s original calculations. Subsequent data caused it to be revised to about 0.85 second of arc. Also, as we shall see, he later revised his theory to predict twice the bending. An arc-second, or second of arc, is an angle of
¹
?3,600 of a degree.

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Here’s how it works. If you are at some point in curved space and want to know the distance to a neighboring point—infinitesimally close—then things can be complicated if you have just the Pythagorean theorem and some general geometry to use. The distance to a nearby point to the north may need to be computed differently from the distance to one to the east or to one in the up direction. You need something comparable to a little scorecard at each point of space to tell you the distance to each of these points. In four-dimensional spacetime your scorecard will require ten numbers for you to be able to deal with all the questions pertaining to spacetime distances to nearby points. You need such a scorecard for every point in the spacetime. But once you have those scorecards, you can figure out the distance along any curve: just add up the distances along each infinitesimal bit using the scorecards as you pass them. These scorecards form the metric tensor, which is a field in spacetime. In other words, it is something defined at every point, but that can have differing values at every point. I am grateful to Professor John D. Norton for helping with this section.

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For clarity, I refer to the boy by both of his given names, Hans Albert, although his father invariably referred to him simply as Albert. At one point, Einstein wrote a letter to his son and signed it “Albert” instead of “Papa.” In his next letter, he awkwardly began, “The explanation for the curious signature on my last letter is that, in my absentmindedness, instead of signing my own name, I frequently sign for the person to whom the letter is addressed” (Einstein to Hans Albert Einstein, March 11 and 16, 1916).

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Einstein’s salary after tax was 13,000 marks. Inflation was beginning to set in, and the value of the German mark had fallen from 24 cents in 1914 to 19 cents in January 1918. One mark at the time would buy two dozen eggs or four loaves of bread. (A year later, the mark would be worth only 12 cents, and when hyperinflation began to rage in January 1920 only 2 cents.) Mari
’s stipend of 6,000 marks in January 1918 was thus worth about $1,140, or just under $15,000 in inflation-adjusted 2006 dollars. His proposal was to increase this by 50 percent.

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Chapter 14 describes Einstein’s revision of this view in a 1920 lecture in Leiden.

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See chapter 14 for Einstein’s decision to renounce the term when he discovered the universe was expanding.

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Described in chapter 14.

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The word Einstein used was
Stammesgenossen.
Although
Stamm
generally means tribe, that translation can have some racial overtones. Some Einstein scholars have said that translations such as “kindred” or “clan” or “lineage” might be clearer.

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I have used the translation preferred by Abraham Pais. Einstein’s words in German were, “Raffiniert ist der Herr Gott, aber boshaft ist er nicht.”

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Governor Channing Cox had been thrust a version of the test earlier that week, and his first three responses were: Where does shellac come from? “From a can.” What is a monsoon? “A funny-sounding word.” Where do we get prunes? “Breakfast.”

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Robert Andrews Millikan would win the Nobel Prize the following year, 1923, for experimental work on the photoelectric effect he had done at the University of Chicago. By then he had become director of the physics lab at the California Institute of Technology, and in the early 1930s he would bring Einstein there as a visiting scientist.

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See page 119 for Newton’s thought experiment about whether water rotating in a bucket in empty space would be subject to inertial pressure and thus press against the sides of the bucket. See page 251 for Einstein’s 1916 view, which he was now revising, that an empty universe would have no inertia or fabric of spacetime.

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The de Broglie wavelength of a baseball thrown at 90 mph would be about 10
^–34
meters, incredibly smaller than the size of an atom or even a proton, so infinitessimal as to be unobservable.

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In 1995, Bose-Einstein condensation was finally achieved experimentally by Eric A. Cornell, Wolfgang Ketterle, and Carl E. Wieman, who were awarded the 2001 Nobel Prize for this work.

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From his 1905 special relativity paper: “It is well known that Maxwell’s electrodynamics—as usually understood now—when applied to moving bodies leads to asymmetries that do not seem inherent in the phenomena. Take, for example, the electrodynamic interaction between a magnet and a conductor.” From the 1905 light quanta paper: “A profound formal difference exists between the theories that physicists have formed about gases and other ponderable bodies, and Maxwell’s theory of electromagnetic processes in so-called empty space.”

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“To be is to be perceived,” meaning that it makes no sense to say that unperceived things—most famously Berkeley’s example of trees in a forest “and no body by to perceive them”—actually exist (George Berkeley,
Principles of Human Knowledge,
section 23).

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As Eddington showed, the cosmological term probably would not have worked even if the universe had turned out to be static. Because it required such a delicate balance, any small disturbance would have caused a runaway expansion or contraction of the universe.

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The pacifists assumed that no other explanation was needed, but some contemporary accounts somehow thought the buttons referred to 2 percent beer.

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There are two related concepts that Einstein uses.
Separability
means that different particles or systems that occupy different regions in space have an independent reality;
locality
means that an action involving one of these particles or systems cannot influence a particle or system in another part of space unless something travels the distance between them, a process limited by the speed of light.

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An aneurysm is the ballooning or dilation of a blood vessel, as if it were blistering. The abdominal aorta is one of the large arteries from the heart, in the region between the diaphragm and the abdomen.